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Matematicheskie Zametki, 2015, Volume 97, Issue 4, Pages 566–582
DOI: https://doi.org/10.4213/mzm9354 (Mi mzm9354) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Structure of the Hopf Cyclic (Co)Homology of Algebras of Smooth Functions

I. M. Nikonova, G. I. Sharyginab

a M. V. Lomonosov Moscow State University
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow
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DOI: https://doi.org/10.4213/mzm9354
Abstract: The paper discusses the structure of the Hopf cyclic homology and cohomology of the algebra of smooth functions on a manifold provided that the algebra is endowed with an action or a coaction of the algebra of Hopf functions on a finite or compact group or of the Hopf algebra dual to it. In both cases, an analog of the Connes–Hochschild–Kostant–Rosenberg theorem describing the structure of Hopf cyclic cohomology in terms of equivariant cohomology and other more geometric cohomology groups is proved.
Keywords: Hopf cyclic homology with coefficients, Hopf cyclic cohomology with coefficients, algebra of smooth functions on a manifold, Hopf algebra of functions on a group, Hopf cyclic complex, equivariant cohomology, module of sections.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00007-a
Ministry of Education and Science of the Russian Federation НШ-581.2014.1
This work was supported by the Russian Foundation for Basic Research (grant no. 14-01-00007-a) and by the program “Leading Scientific Schools” (grant no. NSh-581.2014.1).
Received: 03.03.2012
Revised: 22.11.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 4, Pages 575–587
DOI: https://doi.org/10.1134/S0001434615030281
Bibliographic databases:
Document Type: Article
UDC: 514.7
Language: Russian
Citation: I. M. Nikonov, G. I. Sharygin, “The Structure of the Hopf Cyclic (Co)Homology of Algebras of Smooth Functions”, Mat. Zametki, 97:4 (2015), 566–582; Math. Notes, 97:4 (2015), 575–587
Citation in format AMSBIB
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